Chapter 4: Introduction to Rotating Machines

Example 4.2, Page number: 199

In [1]:
from __future__ import division
from math import *

#Variable declaration:
uo=4*pi*10**-7                          #Permeabolity of free space(H/m)
g=0.7*10**-3                            #Length of air gap(m)
p=4                                     #no. of poles
Ba=1.6                                  #Magnetic flux density(T)
Kr=0.935                                #Winding constant
N=263                                   #No. of turns

#Calculations:
Ir=(pi*g*p/(4*uo*Kr*N))*1.6


#Results:
print "Rotor winding current:",round(Ir,1),"A"

Rotor winding current: 11.4 A

Example 4.3, Page number: 208

In [2]:
from __future__ import division
from math import *

#Variable declaration:
fc=60                                   #frequency of the current(Hz)
p=[2, 4, 6]                             #matrix of no. of poles

#Calculations:
ns=[0]*3
ws=[0]*3
wc=2*pi*fc
for n in range(0,3,1):
    ws[n]=round((2/p[n])*wc,0)
    
for i in range(0,3,1):
    ns[i]=round(120*fc/p[i],0)


#Results:
print "The synchronous angular velocities:",ws, "rad/sec"
print "The speed of the rotor:",ns,"r/min"

The synchronous angular velocities: [377.0, 188.0, 126.0] rad/sec
The speed of the rotor: [3600.0, 1800.0, 1200.0] r/min

Example 4.5, Page number: 212

In [3]:
from __future__ import division
from math import *

#Variable declaration:
Nf=68                                   #Field winding
Na=18                                   #Armature winding
r=0.53                                  #mean air gap radius(m)
l=3.8                                   #Armature winding length(m)
Kf=0.945                                #Winding factor of field winding
Ka=0.933                                #Winding factor of armature winding
g=4.5*10**-2                            #Air gap length(m)
p=2                                     #No. of poles
If=720                                  #field current(A)
uo=4*pi*10**-7                          #Permeability of free space(H/m)
f=60                                    #Frequency curent(Hz)

#Calculations:
Fag1_peak=4*Kf*Nf*If/(pi*p)
Bag1_peak=uo*Fag1_peak/g
Qp=2*Bag1_peak*l*r
Erms=sqrt(3)*sqrt(2)*pi*f*Ka*Na*Qp


#Results:
print "The peak fundamental mmf,Fag1_peak: ",round(Fag1_peak/10000,2),"* 10^4  A.turns/pole"
print "\nThe flux density in the air gap,Bag1_peak: ",round(Bag1_peak,2),"T"
print "\nThe fundamental flux per pole, Qp:" ,round(Qp,2),"Wb"
print "\nThe rms value of open circuit voltage,Erms: ",round(Erms/1000,1),"KV"

The peak fundamental mmf,Fag1_peak:  2.95 * 10^4  A.turns/pole

The flux density in the air gap,Bag1_peak:  0.82 T

The fundamental flux per pole, Qp: 3.31 Wb

The rms value of open circuit voltage,Erms:  25.7 KV

Example 4.8, Page number: 225

In [4]:
from __future__ import division
from math import *

#Variable Declaration:
ns=1800                            #Speed of rotor(rpm)
f=60                                #Frequency(Hz)
g=1.2*10**-3                        #Air gap length(m)
D=0.27                                  #Avg diameter of the gap(m)
Kr=0.976                             #Winding factor
l=0.32                              #Axial length(m)
I=18                                #Rotor current(A)
p=4                                 #No of poles
Nr=786                              #Rotor windings
B_max=1.5                           #Max. flux densiity(T)


#Calculations:
Fr_max=4*Kr*Nr*I/(pi*p)
T_max=p*pi*D*l*B_max*Fr_max/4
wm=ns*pi/30
P=wm*T_max


#Results:
print "Maximum torque, T_max:",round(T_max,0),"Nm"
print "Maximum power,P:",round(P/1000,0),"kW"

Maximum torque, T_max: 1790.0 Nm
Maximum power,P: 337.0 kW

Example 4.9, Page number: 229

In [5]:
from __future__ import division
from math import *

#Variable Declaration:
b=0.5                                       #Wavelength of wnding(m)
l=1.5                                   #Winding length(m)
I=700                                   #Currents in windings(A)
N=45                                    #No. of turns
K=0.92                                  #winding factor
p=3                                     #No. of phases
uo=4*pi*10**-7
g=0.01                                  #Air gap flux(m)
f=25                                    #Frequency of the exciting current(A)

#Calculations:
F_peak=(3*4*K*N*700)/round(4*pi*p,-1)
B=uo*F_peak/g
v=f*b

#Results:
print "Amplitude of the resultant mmf wave:",round(F_peak/1000,1),"kA/m"
print "Peak air gap flux:",round(B,1),"T"
print "Velocity of the travelling wave:",v,"m/s"

Amplitude of the resultant mmf wave: 8.7 kA/m
Peak air gap flux: 1.1 T
Velocity of the travelling wave: 12.5 m/s